FYI, I am using Tmux through the Mac OS X Terminal app.
I found using send-keys -R
to be a little slow - here is another way to clear screen and history with a single command
bind-key C send-keys "clear && tmux clear-history" \; send-keys "Enter"
A nested tmux call is used as the more obvious
bind-key C send-keys "clear" \; send-keys "Enter" \; clear-history
fails to clear the screen's current text from the history - the clear-history command appears to run in a separate thread to send-keys.